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Derivative problem that I thought would be easy

  1. Nov 15, 2013 #1
    I've attached a picture of the problem.

    The problem asks from f'(0) of the function:

    f(x)=e^(2x)*g(x)

    g(0)=-5 and g'(0)=3 are given.

    So the answer I came to was:

    f'(x)=2e^(2x)*g'(x)

    However, when I work out the numbers I get:

    f'(0)=6

    This is not right. So I figured I made a mistake a mistake when taking the derivative of f(x). Now I'm stuck because I'm not sure how to derive the function when g(x) isn't explicitly given.
     

    Attached Files:

  2. jcsd
  3. Nov 15, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Yes, you made a mistake when taking the derivative of f(x). Use the product rule.
     
  4. Nov 15, 2013 #3
    The product rule say that:
    [itex](f(x)g(x))'=f'(x)g(x)+f(x)g'(x)[/itex]
    You did:
    [itex](f(x)g(x))'=f'(x)g'(x)[/itex]
    Which is incorrect.
     
  5. Nov 15, 2013 #4
    Wow, thanks guys. Sometimes sleep deprivation can do some crazy things.
     
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